While American Express Company (AXP 1.12%) and PayPal Holdings Inc (PYPL 0.29%) are rightly thought of as similar companies by investors, the two still have very different business models, valuations, and expectations. This can make true comparisons difficult when looking for ways to invest in payments or fintech companies. With that in mind, let's examine both companies closer to see which is more deserving of your hard-earned investment dollars.

The case for American Express (AXP)

American Express operates a closed-loop credit card system, meaning that it issues its own cards and then facilitates the payments on those cards. This is similar to Discover Financial, but different than Mastercard or Visa which only facilitate payments on cards that other institutions issue. Departing American Express CEO Kenneth Chenault believes this business model gives the company major advantages over other card issuers. At a recent investor conference, he said:

"This is why I believe a diversified integrated business model such as ours, which includes both issuing and network businesses across multiple geographies, products and customer segments offers major advantages ... Our closed loop, which combines information from both our issuing and network businesses gives us access to data that is both broad and deep. Increasingly, the information we analyze in the age of Big Data is a critical ingredient in building value for both card members and merchants."

With the Costco unpleasantness firmly behind it, the future looks brighter for American Express than it has for the last few years. When the company reported its third-quarter results, total revenues net of interest expense increased 9% to $8.4 billion and net income increased 19% to $1.36 billion. Total loans rose to $70.2 billion, a 14% increase year over year. The company also raised its full year 2017 guidance to a new range of $5.80-5.90. At the midpoint of this guidance, that gives American Express a current P/E ratio of about 16.8. That's cheaper than the average P/E ratio across the S&P 500 universe right now.

A man's hand holds credit card against contactless credit card reader over a table with a platter of muffins.

Both PayPal and American Express are trying to stay on top of the latest technology in payments. Image source: Getty Images.

One of the best things going for the company is that it is consistently recognized as having the most loyal and most satisfied customers across the credit card and payments industry. Not only does this make customer retention easier, it is also a source of loan growth. Last quarter, management stated half its loan growth had come from existing account holders. Beyond the benefits of customer retention, this is a cheaper source of loan growth than marketing to look for new card holders.

The case for PayPal (PYPL)

PayPal Holdings has quite the different business model from American Express, especially after the recent sale of its U.S. consumer credit portfolio to Synchrony Financial, a deal that left PayPal with almost no exposure to credit risk. While PayPal has several different platforms, its core service allows users to digitally send peer-to-peer (P2P) payments and make purchases online and, in an increasing number of cases, at the physical point-of-sale (POS). One of the key advantages to PayPal's payments platform is that it is open and agnostic, meaning it is available to any potential customer no matter where they bank, what type of phone they have, or what operating system their phone uses -- key hindering factors in almost all other competing platforms.

PayPal has shown strong revenue and earnings growth. In its third quarter, revenue grew to $3.24 billion, a 21% increase year over year, and non-GAAP earnings per share rose to $0.46, a 31% increase year over year. Using the midpoint of PayPal's fourth quarter earnings guidance, the company's non-GAAP P/E based on its full year 2017 earnings is a shade over 40, a far richer valuation than American Express.

Even better than the company's fattening top and bottom lines, however, is its active account growth and deepening customer engagement. In the company's third quarter, 8.2 million active accounts were added, raising its total to 218 million. Not only is PayPal growing its base of users, but these account holders are increasing their use of the platform. For instance, payment transactions per active account increased 9% year over year in the third quarter.

A bar graph showing the growth of PayPal's account holder engagement.

Not only is PayPal growing its user base, but the engagement level of that user base is increasing too. Image and data source: PayPal Holdings Inc 2017 Q3 Investor Presentation Slideshow.

What makes PayPal exciting is that it has positioned itself extremely well to profit from the rise of e-commerce and m-commerce, transactions facilitated over a mobile device. PayPal's mobile payment volume rose to about $40 billion in its third quarter, good for a 54% increase year over year. Mobile payment volume now makes up 35% of PayPal's total payment volume.

Beyond PayPal's core platform, one of its most exciting other services is Venmo. Venmo started off as a P2P payment platform with a social media twist, but is now being accepted as a method of payment at over two million retailers. Venmo continues to show explosive growth; in the third quarter, Venmo's payment volume rose to $9.4 billion, a 93% increase year over year.

The final verdict

Both of these companies seemingly offer investors attractive targets but, given the choice, I would rather invest in PayPal. American Express is being sold at a discount to the market while finally showing solid earnings growth. As Chenault explained, its business model offers the advantages of capturing lots of card holder data -- virtual gold in today's business world. However, because of the credit risk it faces, even with industry-leading net write-off rates, it will probably never achieve a valuation equal to the market average.

PayPal stands poised to capitalize on too many undeniable trends, like the digitization of money, e-commerce, and mobile commerce, to not choose it over American Express. It also seems to have more future paths to success or, what some Foolish investors refer to as optionality. For instance, if Pay with Venmo shows the same popularity with millennials and growth as Venmo did as a P2P payments platform, it could give PayPal an entire additional leg of growth beyond its core platform. It is for these reasons that I have been a shareholder of PayPal since it was spun off more than two years ago and why I would still choose it over American Express today.